Turning to relative value, we see opportunities in the 2036-38 sector, as these securities have underperformed significantly relative to our par curve over the last 4 weeks. In particular, we like to fade the cheapening in 4.75% Feb-37s (Figure 6). Separately, we note that 4.5% Aug-39s, the CTD into USM4, have outperformed recently, but this security will drop out of the US deliverable basket next week, and likely has room to cheapen. Further, as Figure 7 shows, the Feb-37/ Aug-39 appear 6.9bp too flat relative to the shape of 10s/20s. Against this backdrop, we recommend 100:98 weighted 4.75% Feb 37s / 4.5% Aug 39s steepeners (see Trade recommendations).
In [38]:
import sys
sys.path.append("../../")
In [39]:
from CurveInterpolator import GeneralCurveInterpolator
from CurveDataFetcher import CurveDataFetcher
from utils.rv_utils import cusip_spread_rv_regression
from utils.viz import plot_usts
from models.calibrate import calibrate_mles_ols, calibrate_nss_ols
from models.NelsonSiegelSvensson import NelsonSiegelSvenssonCurve
In [40]:
import pandas as pd
import numpy as np
import scipy
from datetime import datetime
from typing import Dict, List
import tqdm
import matplotlib.pyplot as plt
import matplotlib.pylab as pylab
params = {
"axes.titlesize": "x-large",
"legend.fontsize": "x-large",
"axes.labelsize": "x-large",
"xtick.labelsize": "x-large",
"ytick.labelsize": "x-large",
}
pylab.rcParams.update(params)
import seaborn as sns
sns.set(style="whitegrid", palette="dark")
import nest_asyncio
nest_asyncio.apply()
import warnings
warnings.filterwarnings('ignore', category=FutureWarning)
warnings.filterwarnings('ignore', category=pd.errors.SettingWithCopyWarning)
warnings.filterwarnings('ignore', category=RuntimeWarning)
import plotly
plotly.offline.init_notebook_mode()
%load_ext autoreload
%autoreload 2
The autoreload extension is already loaded. To reload it, use: %reload_ext autoreload
In [41]:
curve_data_fetcher = CurveDataFetcher(use_ust_issue_date=True)
In [42]:
quote_type = "eod"
as_of_date = datetime(2024, 6, 14)
curve_set_df = curve_data_fetcher.build_curve_set(
as_of_date=as_of_date,
sorted=True,
include_off_the_run_number=True,
market_cols_to_return=[f"{quote_type}_price", f"{quote_type}_yield"],
calc_free_float=True,
use_github=True,
)
curve_set_df
Out[42]:
| cusip | security_type | auction_date | issue_date | maturity_date | time_to_maturity | int_rate | high_investment_rate | is_on_the_run | ust_label | ... | parValue | percentOutstanding | est_outstanding_amt | corpus_cusip | outstanding_amt | portion_unstripped_amt | portion_stripped_amt | reconstituted_amt | free_float | rank | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 912797KF3 | Bill | 2024-05-16 | 2024-05-21 | 2024-06-18 | 0.010959 | NaN | 5.365 | False | 5.365% Jun-24 | ... | 8.357725e+08 | 0.003873 | 2.157845e+11 | NaN | 0.000000e+00 | NaN | 0.000000e+00 | NaN | -835.7725 | 16.0 |
| 1 | 912797KG1 | Bill | 2024-05-23 | 2024-05-28 | 2024-06-25 | 0.030137 | NaN | 5.365 | False | 5.365% Jun-24 | ... | 8.312242e+08 | 0.003852 | 2.158075e+11 | NaN | 0.000000e+00 | NaN | 0.000000e+00 | NaN | -831.2242 | 15.0 |
| 2 | 912797KH9 | Bill | 2024-05-30 | 2024-06-04 | 2024-07-02 | 0.049315 | NaN | 5.365 | False | 5.365% Jul-24 | ... | 5.800708e+08 | 0.002822 | 2.055647e+11 | NaN | 0.000000e+00 | NaN | 0.000000e+00 | NaN | -580.0708 | 14.0 |
| 3 | 912797KN6 | Bill | 2024-06-06 | 2024-06-11 | 2024-07-09 | 0.068493 | NaN | 5.365 | True | 5.365% Jul-24 | ... | 5.812060e+08 | 0.002760 | 2.105957e+11 | NaN | 0.000000e+00 | NaN | 0.000000e+00 | NaN | -581.2060 | 13.0 |
| 4 | 912797KP1 | Bill | 2024-05-16 | 2024-05-21 | 2024-07-16 | 0.087671 | NaN | 5.387 | False | 5.387% Jul-24 | ... | 3.064740e+08 | 0.002184 | 1.403087e+11 | NaN | 0.000000e+00 | NaN | 0.000000e+00 | NaN | -306.4740 | 12.0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 387 | 912810TR9 | Bond | 2023-07-13 | 2023-07-17 | 2053-05-15 | 28.936986 | 3.625 | NaN | False | 3.625% May-53 | ... | 5.723292e+09 | 0.091437 | 6.259307e+10 | 912803GS6 | 6.271107e+10 | 42364550.8 | 2.034652e+10 | 2692420.0 | 36641.2589 | 4.0 |
| 388 | 912810TT5 | Bond | 2023-10-12 | 2023-10-16 | 2053-08-15 | 29.189041 | 4.125 | NaN | False | 4.125% Aug-53 | ... | 8.606596e+09 | 0.120247 | 7.157430e+10 | 912803GU1 | 7.158330e+10 | 62241373.0 | 9.341928e+09 | 154800.0 | 53634.7768 | 3.0 |
| 389 | 912810TV0 | Bond | 2024-01-11 | 2024-01-16 | 2053-11-15 | 29.441096 | 4.750 | NaN | False | 4.750% Nov-53 | ... | 4.567153e+08 | 0.006874 | 6.644364e+10 | 912803GW7 | 6.644364e+10 | 57664315.9 | 8.779329e+09 | 3265920.0 | 57207.6006 | 2.0 |
| 390 | 912810TX6 | Bond | 2024-04-11 | 2024-04-15 | 2054-02-15 | 29.693151 | 4.250 | NaN | False | 4.250% Feb-54 | ... | 2.211754e+09 | 0.031064 | 7.119879e+10 | 912803GY3 | 7.119879e+10 | 61771996.7 | 9.426795e+09 | 1365210.0 | 59560.2422 | 1.0 |
| 391 | 912810UA4 | Bond | 2024-05-09 | 2024-05-15 | 2054-05-15 | 29.936986 | 4.625 | NaN | True | 4.625% May-54 | ... | 3.142249e+09 | 0.111657 | 2.814189e+10 | 912803HB2 | 2.814189e+10 | 27729908.5 | 4.119840e+08 | 100200.0 | 24587.6594 | 0.0 |
392 rows × 25 columns
Build Par Curve Model¶
In [43]:
def liquidity_premium_curve_set_filter(curve_set_df: pd.DataFrame):
# remove OTRs, olds, double olds, triple olds
curve_set_filtered_df = curve_set_df[
(curve_set_df["rank"] != 0) & (curve_set_df["rank"] != 1) & (curve_set_df["rank"] != 2) & (curve_set_df["rank"] != 3)
]
# remove TBills
curve_set_filtered_df = curve_set_filtered_df[curve_set_filtered_df["security_type"] != "Bill"]
# remove low free float bonds (< $5bn)
curve_set_filtered_df = curve_set_filtered_df[curve_set_filtered_df["free_float"] > 5000]
# filter out bonds very close to maturity
curve_set_filtered_df = curve_set_filtered_df[curve_set_filtered_df["time_to_maturity"] > 30 / 360]
# remove CTDs
curve_set_filtered_df = curve_set_filtered_df[
~curve_set_filtered_df["cusip"].isin(
[
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.625s 2026-09-15")["cusip"], # TU
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.125s 2027-09-30")["cusip"], # Z3N
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.25s 2029-02-28")["cusip"], # FV
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.25s 2031-06-30")["cusip"], # TY
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.375s 2034-05-15")["cusip"], # TN
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.625s 2040-02-15")["cusip"], # US
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.5s 2044-02-15")["cusip"], # TWE
curve_data_fetcher.ust_data_fetcher.cme_ust_label_to_cusip("4.75s 2053-11-15")["cusip"], # UL
]
)
]
curve_set_filtered_df = curve_set_filtered_df.sort_values(by=["time_to_maturity"])
return curve_set_filtered_df
def no_filter(curve_set_df: pd.DataFrame):
return curve_set_df
In [44]:
# filter and fit bspline w/ knots are liquidity points
curve_set_filtered_df = liquidity_premium_curve_set_filter(curve_set_df=curve_set_df)
filtered_fitted_interpolator = GeneralCurveInterpolator(
x=curve_set_filtered_df["time_to_maturity"].to_numpy(),
y=curve_set_filtered_df[f"{quote_type}_yield"].to_numpy(),
)
fitted_bspline = filtered_fitted_interpolator.b_spline_with_knots_interpolation(
knots=[0.5, 1, 2, 3, 4, 5, 7, 10, 15, 20, 25],
k=3,
return_func=True,
)
nss_func, status_nss, _ = calibrate_nss_ols(
curve_set_filtered_df["time_to_maturity"].to_numpy(),
curve_set_filtered_df[f"{quote_type}_yield"].to_numpy(),
)
assert status_nss
mles_func, status_mles = calibrate_mles_ols(
curve_set_filtered_df["time_to_maturity"].to_numpy(),
curve_set_filtered_df[f"{quote_type}_yield"].to_numpy(),
overnight_rate=5.31,
N=9,
)
In [45]:
plot_usts(
curve_set_df=curve_set_df,
ttm_col="time_to_maturity",
ytm_col=f"{quote_type}_yield",
hover_data=[
"issue_date",
"maturity_date",
"cusip",
"original_security_term",
"ust_label",
f"{quote_type}_price",
"free_float",
],
ust_labels_highlighter=[
("4.750% Feb-37", "red"), ("4.500% Aug-39", "blue"),
],
zero_curves=[(fitted_bspline, "BSpline k=3 - Zero Filtered Fit"), (nss_func, "Nelson Siegel Svensson"), (mles_func, "Merrill Lynch Exponential Spline")],
title=f"All USTs - using {f"{quote_type}_yield"} - as of {as_of_date}",
y_axis_range=[3.9, 5.7]
)
Fetching historical curve sets to regress Feb-37s / Aug-39s vs our fitted model over time (10s/20s par curve)¶
In [46]:
start_date = datetime(2023, 12, 1)
end_date = datetime(2024, 6, 14)
curve_sets_dict_df, fitted_curves_dict = curve_data_fetcher.fetch_historical_curve_sets(
start_date=start_date,
end_date=end_date,
fetch_soma_holdings=True,
fetch_stripping_data=True,
calc_free_float=True,
fitted_curves=[
("LPF", f"{quote_type}_yield", liquidity_premium_curve_set_filter),
("NSS", f"{quote_type}_yield", no_filter, calibrate_nss_ols),
],
)
FETCHING CURVE SETS...: 100%|██████████| 174/174 [00:03<00:00, 53.00it/s] AGGREGATING CURVE SET DFs: 100%|██████████| 174/174 [00:08<00:00, 20.98it/s]
In [47]:
cusip_timeseries: Dict[str, List[Dict[str, str | float | int]]] = {}
fitted_cubic_spline_timeseries: Dict[datetime, scipy.interpolate] = {}
fitted_bspline_timeseries: Dict[datetime, scipy.interpolate] = {}
fitted_smooth_spline_timeseries: Dict[datetime, scipy.interpolate] = {}
nss_timeseries: Dict[datetime, NelsonSiegelSvenssonCurve] = {}
for dt in tqdm.tqdm(curve_sets_dict_df.keys(), desc="Main Loop"):
fitted_cubic_spline = fitted_curves_dict[dt]["LPF"].b_spline_with_knots_interpolation(
knots=[0.5, 1, 2, 3, 4, 5, 7, 10, 15, 20, 25],
k=3,
return_func=True,
)
fitted_bspline = fitted_curves_dict[dt]["LPF"].b_spline_with_knots_interpolation(
knots=[0.5, 1, 2, 3, 4, 5, 7, 10, 15, 20, 25], k=5, return_func=True
)
fitted_smooth_spline = fitted_curves_dict[dt]["LPF"].b_spline_with_knots_interpolation(
knots=[0.5, 1, 2, 3, 5, 7, 10, 20], k=4, return_func=True
)
curr_nss_model = fitted_curves_dict[dt]["NSS"]
fitted_cubic_spline_timeseries[dt] = fitted_cubic_spline
fitted_bspline_timeseries[dt] = fitted_bspline
fitted_smooth_spline_timeseries[dt] = fitted_smooth_spline
nss_timeseries[dt] = curr_nss_model
curr_curve_set_df = curve_sets_dict_df[dt]
curr_curve_set_df["lpf_cubic_spline_spread"] = curr_curve_set_df["eod_yield"] - fitted_cubic_spline(curr_curve_set_df["time_to_maturity"])
curr_curve_set_df["lpf_bspline_spread"] = curr_curve_set_df["eod_yield"] - fitted_bspline(curr_curve_set_df["time_to_maturity"])
curr_curve_set_df["lpf_smooth_spline_spread"] = curr_curve_set_df["eod_yield"] - fitted_smooth_spline(curr_curve_set_df["time_to_maturity"])
curr_curve_set_df["nf_nss_spread"] = curr_curve_set_df.apply(
lambda row: row["eod_yield"] - curr_nss_model(row["time_to_maturity"])
if pd.notna(row["eod_yield"]) and curr_nss_model(row["time_to_maturity"]) is not None
else np.nan, axis=1
)
for _, row in curr_curve_set_df.iterrows():
if row["cusip"] not in cusip_timeseries:
cusip_timeseries[row["cusip"]] = []
payload = {
"Date": dt,
"cusip": row["cusip"],
f"{quote_type}_yield": row[f"{quote_type}_yield"],
f"{quote_type}_price": row[f"{quote_type}_price"],
"lpf_cubic_spline_spread": row["lpf_cubic_spline_spread"],
"lpf_bspline_spread": row["lpf_bspline_spread"],
"lpf_smooth_spline_spread": row["lpf_smooth_spline_spread"],
"nf_nss_spread": row["nf_nss_spread"],
"free_float": row["free_float"],
"est_outstanding_amount": row["est_outstanding_amt"],
"soma_holdings": row["parValue"],
"soma_holdings_percent_outstanding": row["percentOutstanding"],
"stripped_amount": row["portion_stripped_amt"],
"reconstituted_amount": row["reconstituted_amt"],
"lpf_cubic_spline": fitted_cubic_spline,
"lpf_bspline": fitted_bspline,
"lpf_smooth_spline": fitted_smooth_spline,
"nf_nss": curr_nss_model,
}
cusip_timeseries[row["cusip"]].append(payload)
Main Loop: 100%|██████████| 136/136 [00:04<00:00, 29.89it/s]
In [48]:
ct_yields_df = curve_data_fetcher.fedinvest_data_fetcher.get_historical_ct_yields(start_date=start_date, end_date=end_date)
ct_yields_df
Out[48]:
| Date | CT2M | CT3M | CT6M | CT1 | CT2 | CT3 | CT5 | CT7 | CT10 | CT20 | CT30 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2023-12-01 | NaN | 5.403710 | 5.334186 | 5.042904 | 4.558757 | 4.315484 | 4.143857 | 4.218557 | 4.216330 | 4.576711 | 4.405911 |
| 1 | 2023-12-04 | NaN | 5.403306 | 5.365748 | 5.108344 | 4.641114 | 4.406067 | 4.234372 | 4.296414 | 4.281504 | 4.609961 | 4.433200 |
| 2 | 2023-12-05 | NaN | 5.435829 | 5.333398 | 5.064251 | 4.574224 | 4.337521 | 4.143529 | 4.202830 | 4.177950 | 4.482567 | 4.307160 |
| 3 | 2023-12-06 | NaN | 5.424800 | 5.322358 | 5.085874 | 4.606928 | 4.337197 | 4.122480 | 4.156189 | 4.120791 | 4.401424 | 4.224558 |
| 4 | 2023-12-07 | NaN | 5.445638 | 5.365075 | 5.063700 | 4.589782 | 4.325490 | 4.115346 | 4.161244 | 4.135875 | 4.422127 | 4.248954 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 131 | 2024-06-10 | NaN | 5.433394 | 5.395624 | 5.180479 | 4.873234 | 4.670801 | 4.478120 | 4.471751 | 4.464665 | 4.685531 | 4.593689 |
| 132 | 2024-06-11 | NaN | 5.435829 | 5.384512 | 5.179969 | 4.822587 | 4.613020 | 4.407372 | 4.398472 | 4.393831 | 4.622359 | 4.530630 |
| 133 | 2024-06-12 | NaN | 5.435423 | 5.373403 | 5.146778 | 4.755053 | 4.532165 | 4.322755 | 4.309956 | 4.315652 | 4.559851 | 4.474091 |
| 134 | 2024-06-13 | NaN | 5.424395 | 5.365075 | 5.072888 | 4.687455 | 4.451388 | 4.238426 | 4.232236 | 4.241883 | 4.495627 | 4.399851 |
| 135 | 2024-06-14 | NaN | 5.423183 | 5.363884 | 5.060774 | 4.686301 | 4.451066 | 4.223883 | 4.205947 | 4.206966 | 4.460174 | 4.341321 |
136 rows × 12 columns
In [49]:
label1 = "4.750% Feb-37"
label2 = "4.500% Aug-39"
cusip_spread_rv_regression(
curve_data_fetcher=curve_data_fetcher,
label1=label1,
label2=label2,
cusip_timeseries=cusip_timeseries,
fitted_splines_timeseries_dict={
"lpf_cubic_spline": fitted_cubic_spline_timeseries,
"lpf_bspline": fitted_bspline_timeseries,
"lpf_smooth_spline": fitted_smooth_spline_timeseries,
"lpf_smooth_spline": fitted_smooth_spline_timeseries,
},
benchmark_tenor_1=10,
benchmark_tenor_2=20,
ct_yields_df=ct_yields_df
)
lpf_cubic_spline is Benchmark Spline
OLS Regression Results
=========================================================================================
Dep. Variable: 4.750% Feb-37 / 4.500% Aug-39 R-squared: 0.558
Model: OLS Adj. R-squared: 0.554
Method: Least Squares F-statistic: 168.8
Date: Sun, 06 Oct 2024 Prob (F-statistic): 1.72e-25
Time: 19:02:57 Log-Likelihood: 367.53
No. Observations: 136 AIC: -731.1
Df Residuals: 134 BIC: -725.2
Df Model: 1
Covariance Type: nonrobust
===========================================================================================
coef std err t P>|t| [0.025 0.975]
-------------------------------------------------------------------------------------------
const -0.0028 0.013 -0.220 0.826 -0.028 0.023
lpf_cubic_spline_10s20s 0.3968 0.031 12.994 0.000 0.336 0.457
==============================================================================
Omnibus: 23.341 Durbin-Watson: 0.124
Prob(Omnibus): 0.000 Jarque-Bera (JB): 32.796
Skew: -0.911 Prob(JB): 7.56e-08
Kurtosis: 4.570 Cond. No. 25.6
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
=========================================================================================
Dep. Variable: 4.750% Feb-37 / 4.500% Aug-39 R-squared: 0.348
Model: OLS Adj. R-squared: 0.343
Method: Least Squares F-statistic: 71.47
Date: Sun, 06 Oct 2024 Prob (F-statistic): 4.20e-14
Time: 19:02:58 Log-Likelihood: 341.15
No. Observations: 136 AIC: -678.3
Df Residuals: 134 BIC: -672.5
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0635 0.012 5.355 0.000 0.040 0.087
CT10-CT20 0.3652 0.043 8.454 0.000 0.280 0.451
==============================================================================
Omnibus: 47.043 Durbin-Watson: 0.080
Prob(Omnibus): 0.000 Jarque-Bera (JB): 94.403
Skew: -1.531 Prob(JB): 3.17e-21
Kurtosis: 5.698 Cond. No. 27.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Using lpf_cubic_spline for UST Metrics Calcs
4.750% Feb-37 Metrics Calc: 136it [00:03, 36.24it/s] 4.500% Aug-39 Metrics Calc: 136it [00:03, 34.58it/s]
